The Londoners could have taken the lead in the fourth minute when Jodi Jones cut in from the right but his effort from 25 yards was easily saved by Scott Davies.
With 17 minutes on the clock the Daggers had big appeals for a penalty turned down after Ade Yusuff was tripped in the box.
Matt Partridge opened the scoring in the 20th minute with his first professional goal, heading home a Raymond corner from the right.
Within 90 seconds of the restart, the hosts were 2-0 up as Jamie Cureton poked home in the box following a raking pass from Raymond.
The 22-year-old added his name to the scoresheet with a beautiful free-kick from the edge of the area in the 67th minute.
Jones sealed the win in the final minute of the game, tapping home from six yards after Cureton laid the ball back.